# Cylindrically Symmetric Spiraling Accretion in Power-law and Logarithmic Potentials

## TL;DR

This paper investigates cylindrically symmetric steady-state accretion of polytropic matter onto a symmetry axis in power-law and logarithmic potentials, providing exact solutions and qualitative insights into the accretion process.

## Contribution

It introduces a model for cylindrically symmetric accretion, deriving exact solutions using Lambert W functions and analyzing the process in non-spherical potentials.

## Key findings

- Exact solutions for isothermal accretion in power-law potentials
- Exact solutions for polytropic accretion in logarithmic potentials
- Qualitative understanding of accretion in cylindrical symmetry

## Abstract

We study cylindrically symmetric steady-state accretion of polytropic test matter spiraling onto the symmetry axis in power-law and logarithmic potentials. The model allows one to qualitatively understand the accretion process in a symmetry different from that of the classical Bondi accretion. We study the integral curves as level lines of some Hamiltonian and also apply this method to Bondi accretion. The isothermal solutions in power-law potentials (as well as in any radius-dependent potential) can be expressed in exact form in terms of the Lambert W function, while in the case of logarithmic potential, exact solutions can be found for any polytropic exponent.